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Full text of "Speed Conrol of Separately Excited dc Motor using Fuzzy Technique"

ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 201 1 



Speed Conrol of Separately Excited dc Motor using 

Fuzzy Technique 

Ram kumar karsh 1 , Dr. GK.Choudhary 2 , Chitranjan Kumar 3 

'Dept. of Electrical Engineering, NIT Patna, India 

1 tnramkarsh@gmail.com 

2 H.O.D, Dept. of Electrical Engineering, NIT Patnajndia 

(girishkrchoudhary, chitranjan_kumar24) @yahoo.co.in 



Abstract- This paper presents the speed control of a separately 
excited DC motor using Fuzzy Logic Control (FLC). The Fuzzy 
Logic Controller designed in this study applies the required 
control voltage based on motor speed error (e) and its change 
(ce). The performance of the driver system was evaluated 
through digital simulations using Simulink. The simulation 
results show that the control with FLC outperforms PI control 
in terms of overshoot, steady state error and rise time. 
Keywords: DC motor, chopper, FLC. 

I. Introduction 

DC motors are used in many applications like electric 
trains, vehicles, cranes and robotics manipulators. They 
require controlling of speed to perform their tasks. Initially 
speed control of DC motor has been done by voltage control 
[1]. Semiconductors too like MOSFET, IGBT and GTO have 
been used as switching devices to control speed[2]. 

Due to nonlinearity properties, control of system is 
difficult and mathematically tedious. To overcome this 
difficulty, FLC (Fuzzy Logic control) has been developed. 
FLC is applicable to time variant and nonlinear. Metro system 
in the sendia of japan is the best application [3]. 

In this study, the speed response of a separately excited 
DC motor exposed to fixed armature voltage is studied for 
both loaded and unloaded operating conditions. Performance 
of separately excited DC motor is compared for both methods 
FLC and PI controller for both loaded and unloaded 
conditions. In this study, chopper circuit has been used as a 
motor driver. 

II. Motor model 

The resistance of the field winding and its inductance are 
represented by R f and L respectively. The armature, resistance 
and inductance are represented by R and L respectively. 
Armature reactions effects are ignored in the description of 
the separately excited DC motor. This negligence is justifiable 
to minimize the effects of armature reaction since the motor 
(SE) used has either interpoles or compensating winding. 
The fixed voltage V is applied to the field and the field current 
settles down to a constant value. A linear model of a simple 
separately excited DC motor consists of a mechanical equation 
and electrical equation as determined in the following 
equations: 



©2011 ACEEE 
DOI:01.DEPE02.03.533 



J, 



d(a n 
dt 



^„(pIa-bco m -M 



load 



L 



dt 



V -I.R -K h 0co 



(1) 



(2) 



The dynamic model of the system is formed using these 
differential equations and Matlab Simulink blocks as shown 
in Fig. I, 



31 



%:•. 



<:> 



I — y^ 



o- 



_Si- 



:j 



iijiii 



©- 



i 



■ 



;.-; 



■.» 



mjmti 



C" 



i: j : 



«■♦ 



+0 



Fig 1: Simulink Motor mode] 
Table I. Motor Parameters 





Parameter 


Description 


Value 




Ra 


Armature 
Resistance^) 


0.5 


L= 


Armature 
Inductance (H) 


0.003 


J* 


Inertia of 
rvlotor{kg.m- ■*' £-) 


0.0167 


K 


Motor 

c onstantfNm' Amp) 


O.S 


B 


D amping ratio of 

mechanical 

systemptas) 


0.0167 



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ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 201 1 



III. Fuzzy Logic Controller (FLC) Description And Design 

Fuzzy logic control is based on logical relationships like 
"suitable, not very suitable, high, little high, much and far 
too much that are frequently used words in people's life. 
Fuzzy Sets Theory has been introduced to express and process 
fuzzy knowledge [4], [5] which are used to show linguistic 
variables. The relation between fuzzy logic and fuzzy set 
theory that is similar that of relation between Boolean logic 
and set theory. Fig. 2 shows a basic FLC structure. 

Fully™*! 



"♦PUfflHlHJlg 



fasfaaw 






■;';.= 






- 



PW-prMaflf 



Fig. 2 Process Blocks for a Fuzzy Controller 

FLC is processed for linguistic definitions, while other 
contrllers work on the accuracy and parameters of system 
model. While designing FLC, there is no need of knowledge 
of system model, as a controller. However, less knowledge of 
control process may result unsatisfactory [6]. 

A. Defining inputs, outputs: 

As the bigger speed error the bigger controller input is 
expected. So, FLC is designed to minimize speed error. Due to 
that FLC uses error (e) and change of error (ce) for linguistic 
variables which are generated from the control rules. Control 
variable (cu) is applied to achieve angular value (alpha), which 
determines duty cycle. 



e(k)=[co(k)-co(k)]*K 



IE 



ce(k)=[e(k)-e(k-l)]*K 



ca(k)=[a(k)-a(k-l)]*K 



2CE 

3 co. 



(3) 



Here K 1E K, CE and K 3 ca are each gain coefficients and K is a 
time index. 



wr[k] 



9 



-&>■% 



hH 



(UilYWrtlr* 



%MflW 



N 



Fig. 3. Block diagram of the DC motor control 

At nominal value of motor speed the error (e) gives its smallest 
value, and at maximum value of motor speed the error gives 
its larger value, with range -200 and 200. 



©2011 ACEEE 
DOI:01.DEPE.02.03.533 



1 






eHH^**rtr|^ 










^ A/Y^^* - ' — 


-QJ2-L-- 


~rg 


^J-¥--"- 


+ ,[. 


-4J 


— ™ t- i : - t j™ 


a = 


\ 


I 


...., .j 1 ;.,,.._ _j.„, j..^ 


n n 


1 


M 


z : 


■i 


1 


w 


:iziz:jz:iz::n ... 1 ...: 


-1 7 


1 


I- 


■ -1 


\ 


r 


— ; - ; [ t H 


1 h 


- 1 


F+- 








Fig. 4. Change of Error 




W- 





Ai 


A^ 


As 


A. 


A 5 


A« 


A? 


M 


As 


Am 


e 


+ 


- 


- 





- 


- 


- 


+ 


+ 


- 


ce 


- 


- 


— 


— 


- 


- 


— 


+ 


- 


- 



Fig. 5. Dynamic Signal Analysis 
B. Defining membership functions and rules: 

System speed comes to reference value by means of the 
defined rules. For example, first rule on Table determines, 'if 
(e) is PL and (ce) is PL than (c.) is NL According to this rule, 
if error value is positive large and change of error value is 
positive large than output, change of alpha will be negative 
large. In this condition, corresponding A4 interval in Fig 5, 
motor speed is smaller than reference speed and still wants 
to decrease strongly. This is one of the worst conditions in 
control process. Because of the fact that alpha is smaller 
than the required value, its value can be increased by giving 
output PL value. This state corresponds to motor voltage 
decreasing. All conditions in control process are shown in 
Fig.5. Membership functions have been used to convert 
inputs and outputs from crisp value to linguistic term. 
Linguistic terms are represented here by seven membership 
functions shown in table. 



. 




Fig. 6. Linguistic rules for angle (alpha) determination for driver 
circuit. It will for a) speed error, b) Change in speed error, c) 



32 



Change of alpha 



ACEEE 



ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 201 1 







Table II. The Rule Data 


Base 






ee 


m 


NM 


XS 


Z 


PS 


PM 


PL 


m. 


PL 


PL 


PL 


PL 


mi 


2 


2 


XM 


PL 


PL 


PL 


P.I/ 


PS 


2 


2 


m 


PL 


PM 


PS 


PS 


PS 


2 


2 


z 


PL 


PM 


Pi 


2 


NS 


KM 


KL 


p& 


2 


2 


KM 


KS 


KS 


KM 


M 


PM 


2 


2 


NS 


KM 


KL 


M 


M 


PI 


2 


2 


MM 


M 


M 


M 


M 



IV. Driver circuit and modeling 

DC chopper has been used to drive the motor also changes 
average value of load voltage applied from a fixed DC source 
by switching a power switch. 



I. 



y. 



Vo 



Load 



Vo 



i ton, 
■* — *■■*■ 



i©r 



■-\ 



I 



Fig 7. Operating principle and output waveform of Driver 

Using Fig 7, the average output voltage can be calculated as 



V 



t, 



do 



t +t« 

l on I off 



-V 



(4) 



Where V is the DC source voltage, v, can be controlled 

o do 

using three methods: 

*Hold t fixed and change t (frequency modulation) 

*Hold period (t + t ff ) fixed and change t ff /t rate (pulse 

width modulation) 

*change t fl and t separately. (Combination of first and 

second method) 

One-quadrant DC chopper and general waveforms for 

continuous current conditions are shown in fig. 8 



(Xjwi: nflcli 




Fig 8. simple power circuit of a one quadrant DC chopper 



10 



« 



imax 




irm 



iD 



imin 



Vo 



DT 



fr 



I 



0T T 

Fig 9. General waveform for current continuous condition 




Fig. 10. DC Chopper model 

Fundamentally, the operating principle of driver model is 
based on the comparison of two signals [7] . One of the sig- 
nals is a triangular waveform which represents one PWM is 
used to control average output voltage period of 2 KHz chop- 
ping frequency and other one is fixed linear signal which 
represents time equivalent of alpha triggering (t ). Since 
chopping frequency is 2 KHz, the amplitude of triangular 
waveform starts from zero and reaches 1 / 2. 10 3 = 0.0005 value. 
On the other hand, the alpha signal from controller is multi- 
plied by 0.0005/360 value to calculate the time corresponding 
to this angle. Alpha signal and triangular signal are Uj and 
U2 variables of ' IF' block used in simulation model shown in 
Fig. 10, respectively. 
•.+ 



OuOOOS 



v ... 
vdo- 




IN 



1 tfs} — ' 

Fig 11. input and output signal of driver model 



©2011 ACEEE 
DOL01.DEPE.02.03.533 



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^ACEEE 



ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 201 1 



V. Control simulation 

In FLC model gainl, gain2 and gain3 define change of error, 
error and change of alpha scaling factors respectively. Simu 



lation results are shown for 50 nm load applied at 0.6s. Simu- 
lation result for PI controller for loaded and no loaded condi- 
tion is shown in table iii 



IZZ1 





S:tf*2 




Aitf 




f I 












I ) 


















■ 














M 




■ -.- 


■ 










' .... . ■:-. 


H» 









r 



:n 



Slit*' 



Fig 12. Fuzzy Logic Controller Simulink model 




Fig 13. a) Speed response of PI controller for used motor 




Fig 13. b) Speed response of Fuzzy controller for used motor 
Table III performance analysis of system 

CI: Kp=100, Ki=15 Tr: Rise time 

C2: Kp=200,Ki=25 e : Steady state error 

C3: Kp=300, Ki=28 %M Percentage Maximum overshoot 

C4: Kp=500, Ki=30 CI, C2 Different Kp and Ki 

coefficients 

(a) For different loads 



p 
I 


Land 


Jtf.Y 


soy 


5GX 


CI 


SO£ 


5.955 


y.Cii 


5 52 


■?„ 


-0.5Q5 


-0.2SS 


-0.131 


C2 


'A.% 


5.655 


5. till 5 


5.631 


s„ 


-6,25 


-D.15S 


-0.15 


C3 


%14 


5. '31 5 


5:7315 


5:7315 


s„ 


-0.1S 


-0.15 


-0.12 


C4 


%u. 


i.S5S 


5.5S5 


5.S95 


■?„ 


-6.1175 


-0.05 


-0.075 


FLC 


5fl4 


0.S1 


2.64 


4.53 






•Br, 


Q.QOdl 


-0.0045 


-0.01S 



(b) Unloaded operation 



Criteria 


PI 


FLC 


CI 


C2 


CS 


C4 


Tr 


0.141 


0.141 


'■ !-i! 


0.141 


0.036 


#r, 


-0.533 


-0.5 '5 


-0.415 


-0.262 


-0.01 


&w f 


5.527 


5.631 


5:711 


5.S94 


0.6S 



Percent overshoot (%M ) and steady state error (e ) are 
measured for different load. 

Conclusion 

Fuzzy Logic Controllers are a suitable option to make 
speed regulation in DC motors and AC motors. The quality of 
the control obtained with FLC's at the first tries is commonly 
good because is based on the knowledge of an expert. It can 
not be said the same about conventional controllers. The 
single human based reasoning used on a FLC can be very 
useful to overcome nonlinearities of any kind of plants in a 
logical way. The experience gained from these works has 
allowed us to attack another systems of very different nature 
obtaining satisfactory results. Comparison between PI 
controller responses and FLC responses is shown in table iii 
and shows that FLC gives better performance than PI 
controller in terms of overshoot , steady state error and rise 
time. Also show that FLC is more sensitive to load changes. 
It would be necessary to use a more complex intelligent control 
system, i.e. Adaptive Fuzzy System, Neuro-Fuzzy System, in 
order to obtain a better performance on speed control 

Refrences 

[I] Chan, C. C, Low Cost Electronic Controlled Variable Speed 
Reluctance Motors, IEEE Transactions on Industrial Electronics, 
Vol. IE-34, No. I. 95-100. February 1987. 

[2] Khoei, A.. Hadidi, Kh., Microprocessor Based Closed-Loop 
Speed Control System for DC Motor Using Power Mosfet. 
Electronics Circuits and Systems IEEE international Conference 
ICECS'96, Vol. 2, 1247-1250, 1996. 

[3] C. Elmas, "Fuzzy Logic Controllers", Seqkin Publishing, April- 
2003 

[4] L. A. Zadeh, " Fuzzy Sets" Informal Control, -01. 8p, p 338- 
353, 1965. 



©2011 ACEEE 
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ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 201 1 



[5] L. A. Zadeh, '. Outline of a new approach to the analysis 

complex systems and decision processes" IEEE Trans. Syst. Man 

Cybem, vol. SMC-3, pp. 2844, 1973 

[6] Y. Tipsuwan, Y. Chow, "Fuzzy Logic Microcontroller 

Implementation for DC Motor Speed Control". IEEE. 1999. 

[7] F. Rahman, .'Lectures 18 Control of E€-DC Conveners", Power 

Electronics. ELEC424019240. 

Ram kumar Karsh was born in 1986 in 
a small village of lanjgir-champa district 
of Chattisgarh. He received B.E. (Electron- 
ics & Tele communication) in 2009 with 
first class from Govt Engineering College, 
Bilaspur, India. He is pursuing M.Tech. 
degree with specialization Control Sys- 
tems from Department of Electrical Engi 

neering, National Institute of Technology (NITP), Patna, India. 
His field of interest includes fuzzy logic, control systems. 





Prof. Girish Kumar Choudhary was born 
in August, 1959 in a small village. He did his 
matriculation in 1975, and was enrolled for 
diploma in Electrical Engineering in the same 
year. He completed his diploma in Electrical 
Engineering securing first position in the 
state of Bihar in 1979. He got his B.Sc 

(Engineering) degree in Electrical in 1985 securing first class first 
from Patna University, Patna with distinction. He acquired his 
Ph.D degree in 1998 from Patna University. He joined BCE Patna 
(Presently NIT Patna) in Ian. 1988 as Lecturer in Electrical 
Engineering and promoted as Associate Professor Electrical 
Engineering in 1996. Subsequently he became Professor in 2006. 
Presently he is working as Professor & Head of Electrical 
Engineering at NIT Patna. He is also holding the post of Chairman, 
HMC, NIT Patna. He has many publications in National and 
International lournals and Conferences. He has also achieved the 
distinction of getting his research product "Adapters for Laptops 
and others Electronic Devices." Patented (No. 235642 dated 
10.07.2009). Prior to joining NIT Patna he has also worked in All 
India Radio (AIR) Patna and Videsh Sanchar Nigam Limited, Arvi, 
Pune. 

Chitranjan kumar received B.E. (Elec- 
tronics & Tele communication) in 2009 
with first class from D.K.TE.S Ichalkaranji 
,Kolhapur, India. He completed M.Tech. 
degree with specialization Control Systems 
in 2011 with first class from Department 
of Electrical Engineering from National In 

stitute of Technology (NITP), Patna, India. His field of interest 
includes fuzzy logic, signal processing, control systems 




©2011 ACEEE 
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^ACEEE